Control and Instrument Variables

[John Marburg]

Hello,

If have got an ecometric question regarding the 2sls approach.

Is it appropriate to use a variable as instrument which is highly correlated to an control variable?

In my case i have the following regression: xtivreg2 TobinsQ (instiutionalholding = tradingvolume, commonsharesoutstanding) firm size debtassetratio r&d sales current ratio i.country i.year i.industry, fe robust

My question regards to the connection between commonsharesoutstanding and firm size which are highly correlated, about 0.86, is this an issue?


Best regards


John Marburg

[Joro Kolev]

In general yes, your instrument can be, and most of the time is, correlated with the included control variables.

I do not see any conceptual problem here if they are highly correlated. You assume that both the control and the instrument are exogenous, so I do not see a conceptual problem of them being highly correlated.

You might run into practical problems if your instrument does now have any explanatory power, when the correlated control is included. You can see this from the first stage.

[John Marburg]

Hello Joro Kolev,

and tank your for the response. If I view the results from the regression, the f statistic seems plausible, only the Hansen J statistic concerns me. Is the rejection of the Hansen j statistic an argument to change my instruments or is it only a weak concern and still plausible?



---------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 102.290
Chi-sq(3) P-val = 0.0000
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 46.273
(Kleibergen-Paap rk Wald F statistic): 34.331
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 14.651
Chi-sq(2) P-val = 0.0007
-endog- option:
Endogeneity test of endogenous regressors: 0.068
Chi-sq(1) P-val = 0.7944

[Jeff Wooldridge]

Your partial output doesn't correspond to your original command. Originally, you have one more IV than needed, which means one overid restriction. But the output shows two overid restrictions.

You'll get a better answer by showing the full output. The above rejects the exogeneity of the IVs and you'll have a hard time convincing others of the findings.

[John Marburg]

Hello Jeff Wooldrige,

i misstakly copied the wrong output and first equation is also now slightly adjusted. Now the following should be correct. But my question remains, with test showing postive exogeneity but HansJ has been rejected. Should i be concernd about HansJ rejected or are a the findings still plausible?


xtivreg2 TobinsQ (SumHoldingsPct= SharesTurnover SharesOutstand HistoricBeta ) DebtTotalAssets RD Marketcap Dividend CurrentRatio SalesGrowth QuickRatio year1 year2 year3 year4 year5 year6 year7 year8 year9 year10 year11 year12 year13 year14 year15 year16 year17 year18 year19 year20 country1dummy country2dummy country3dummy country4dummy Industry1 Industry2 Industry3 Industry4 Industry5 Industry6 Industry7 Industry8 Industry9 Industry10, fe robust endog(SumHoldingsPct)



FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 505 Obs per group: min = 2
avg = 5.2
max = 20
Warning - collinearities detected
Vars dropped: year20 country3dummy country4dummy Industry1 Industry2 Industry3
Industry4 Industry5 Industry6 Industry7 Industry8 Industry9
Industry10

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity

Number of obs = 2621
F( 29, 2087) = 9.93
Prob > F = 0.0000
Total (centered) SS = 1850.552444 Centered R2 = 0.1445
Total (uncentered) SS = 1850.552444 Uncentered R2 = 0.1445
Residual SS = 1583.16186 Root MSE = .865

---------------------------------------------------------------------------------
| Robust
TobinsQ | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
SumHoldingsPct | .0092136 .0139191 0.66 0.508 -.0180673 .0364945
DebtTotalAssets | 1.411096 .2992226 4.72 0.000 .8246308 1.997562
RD | .0709141 .2187299 0.32 0.746 -.3577886 .4996168
Marketcap | .4034193 .0630221 6.40 0.000 .2798983 .5269402
Dividend | -.9168429 .9436319 -0.97 0.331 -2.766327 .9326415
CurrentRatio | -.0308697 .0301671 -1.02 0.306 -.089996 .0282567
SalesGrowth | -.0431051 .0311334 -1.38 0.166 -.1041255 .0179153
QuickRatio | .0430155 .0337949 1.27 0.203 -.0232212 .1092522
year1 | 1.211421 .4978552 2.43 0.015 .2356427 2.187199
year2 | 1.211415 .4456676 2.72 0.007 .337922 2.084907
year3 | .961805 .4795988 2.01 0.045 .0218087 1.901801
year4 | .7652285 .4965268 1.54 0.123 -.2079462 1.738403
year5 | .8623094 .5681948 1.52 0.129 -.2513319 1.975951
year6 | .9297732 .5866466 1.58 0.113 -.2200331 2.079579
year7 | 1.064361 .5814592 1.83 0.067 -.0752779 2.204
year8 | .8454914 .3500931 2.42 0.016 .1593215 1.531661
year9 | 1.043884 .352201 2.96 0.003 .3535828 1.734185
year10 | .698261 .3537709 1.97 0.048 .0048829 1.391639
year11 | .1803058 .2140999 0.84 0.400 -.2393224 .599934
year12 | .0668227 .159486 0.42 0.675 -.2457642 .3794095
year13 | .1048394 .1580006 0.66 0.507 -.204836 .4145149
year14 | .056549 .1771918 0.32 0.750 -.2907406 .4038385
year15 | .100864 .1665984 0.61 0.545 -.2256629 .4273908
year16 | .0353162 .1150414 0.31 0.759 -.1901608 .2607932
year17 | .143305 .1129084 1.27 0.204 -.0779914 .3646014
year18 | .1129019 .1058276 1.07 0.286 -.0945163 .3203202
year19 | .1839287 .1098688 1.67 0.094 -.0314103 .3992677
year20 | 0 (omitted)
country1dummy | -.2832622 .1636203 -1.73 0.083 -.6039521 .0374277
country2dummy | .065858 .3356547 0.20 0.844 -.5920131 .7237292
country3dummy | 0 (omitted)
country4dummy | 0 (omitted)
Industry1 | 0 (omitted)
Industry2 | 0 (omitted)
Industry3 | 0 (omitted)
Industry4 | 0 (omitted)
Industry5 | 0 (omitted)
Industry6 | 0 (omitted)
Industry7 | 0 (omitted)
Industry8 | 0 (omitted)
Industry9 | 0 (omitted)
Industry10 | 0 (omitted)
---------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 9.783
Chi-sq(3) P-val = 0.0205
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 5.189
(Kleibergen-Paap rk Wald F statistic): 3.349
Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 13.91
10% maximal IV relative bias 9.08
20% maximal IV relative bias 6.46
30% maximal IV relative bias 5.39
10% maximal IV size 22.30
15% maximal IV size 12.83
20% maximal IV size 9.54
25% maximal IV size 7.80
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 8.196
Chi-sq(2) P-val = 0.0166
-endog- option:
Endogeneity test of endogenous regressors: 0.401
Chi-sq(1) P-val = 0.5268
Regressors tested: SumHoldingsPct
------------------------------------------------------------------------------
Instrumented: SumHoldingsPct
Included instruments: DebtTotalAssets RD Marketcap Dividend CurrentRatio
SalesGrowth QuickRatio year1 year2 year3 year4 year5 year6
year7 year8 year9 year10 year11 year12 year13 year14
year15 year16 year17 year18 year19 country1dummy
country2dummy
Excluded instruments: SharesTurnover SharesOutstand HistoricBeta
Dropped collinear: year20 country3dummy country4dummy Industry1 Industry2
Industry3 Industry4 Industry5 Industry6 Industry7
Industry8 Industry9 Industry10
------------------------------------------------------------------------------

[Eric de Souza]

Your output is very difficult to read as it is. You should wrap code tags around your output

[Jeff Wooldridge]

John: When the overidentification test rejects, the exogeneity test is pretty meaningless. Your instruments do not pass exogeneity and that is a requirement to test whether the explanatory variable is endogenous.

[John Marburg]

Hello Jeff thank you for your responses, it helps me so much! Despite, If have got further question in regard to the equation above.

I also want to test if there is a non linear relationship between Tobins Q SumHoldingsPct, by using following pattern:

xtivreg2 TobinsQ (SumHoldingsPct SumHoldingsPctsquared= SharesTurnover SharesOutstand)..... control variables



1. Can i still use the instrument variable approach and instrument both SumHoldings and SumHoldingsPctsquared in this way, is this approbiate?

2. Do i need in case of two instrumented variables (SumHoldingsPct SumHoldingsPctsquared) always more than one suitable instrument ? If this is the case, what can i do if i only have one fitting instrument?

3. Is it a better choice to transform the dependent variable, for example ln(TobinsQ) to achieve plausible results in case of non linear relationsship or should i test both approaches?